Mathematical Model of a Buckled Spring for Vehicle Active Suspension

The basic characteristic of a conventional spring is that of a constant rate, that is a linear force-displacement relationship. If, however, a flat, thin leaf spring is end-loaded past its buckling point it will deform into a curve and the resulting force-displacement relationship can be made virtually flat; that is a very low effective rate is seen, once the buckling force is exceeded. A novel form of automotive active suspension system proposed by Leighton & Pullen (1994) relies upon the “buckled spring” element acting through a variable geometry wishbone assembly to provide wheel to body forces that are controllable by a low power actuator but are virtually independent of wheel to body displacement. The dynamic behavior of the spring element is also significant, since resonance effects may affect the vibration isolating properties of the suspension system and may result in unstable modes of motion. This paper presents a rigorous derivation of the static and dynamic characteristic of the spring element and of the effect of design compromises that are essential for practical application. Comparison of the experimental and simulation results shows that the simulation can be used to predict the static and dynamic performance of the spring.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

The Double Seesaw Oscillator in a Windfield: Theory and Experiments

In this paper the dynamics of an oscillator with two degrees-of-freedom of a double seesaw type in a windtunnel is studied. Model equations for this aeroelastic oscillator are derived and an analysis of these equations is given for the non-resonant case. A typical result is a (local codimension two) bifurcation which describes the transfer from the unstable equilibrium state to one of the two normal modes of the oscillator. Some experimental results are presented from which on may conclude that more accurate model equations should be developed.

Efficient Structural Acoustic Analysis Using Finite and Infinite Elements and Parallel Processing Architectures

The analysis of three-dimensional shell structures submerged in an infinite fluid and subjected to arbitrary loadings is a computationally demanding problem regardless of the analytical technique used. Over the past several years, we have developed a combined finite/infinite element method of solving this class of problems that is more efficient than other available techniques, and have implemented it in a comprehensive set of computer programs called SARA. This paper presents an overview of our work in parallizing this software. In the first part of the paper, we describe our method for solving the fluid-structure interaction equations including infinite element theory, and modeling practices that have evolved for solving cylindrical geometries. The second part of the paper addresses parallalization of SARA-3D on both shared and distributed memory architectures. The SARA implementation of the method is described along with sample problems, and a comparison to a SARA-3D solution is provided.

Nonlinear Vibrations in an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Rectangular Tank

The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a rectangular tank, partially filled with liquid, are investigated. The structure containing the tank is vertically subjected to a sinusoidal excitation. In the theoretical analysis, the resonance curves for the responses of the structure and liquid surface are presented by the harmonic balance method, when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. From the theoretical analysis, the following predictions have been obtained: (a) Due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface, (b) the shapes of the resonance curves markedly change depending on the liquid depth, and (c) when the detuning condition is slightly deviated, almost periodic oscillations and chaotic oscillations appear at certain intervals of the excitation frequency. These were qualitatively in good agreement with the experimental results.

Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

Acoustic Double Holography Method and its Application to Engine Noise Research

The acoustic holography (AH) method with single measuring plane has been well known as the conventional method and can be implemented by far field measurement with simple instruments. However, the noise source resolution of the AH is not sufficient. In order to improve the resolution in the noise source identification, several kinds of the acoustic holography methods have been so far proposed. For example, the near field acoustic holography (NAH) can provide high and accurate resolution of the holography by the nearfield measurement. However, the nearfield measurement within one wave length is sometimes impossible in the actual circumstances. The Acoustic Double Holography (A D H) proposed in this paper is a simplified approach with higher resolution of the noise source locations than that of the conventional AH methods. The ADH method basically uses dual measuring planes and does not require nearfield measurement. The sound pressure data detected on the rear plane are transformed into the virtual pressure data on the front plane taking into account of the distance between the plane and the object. Comparing the virtual pressure data with the actual data measured on the front plane, resolution on holography can be improved significantly. Computer simulation and an experiment with two loud speakers were executed in order to confirm the fundamental feature of the proposed method. Several advantages on the method with respect to resolution over the conventional AH method were discussed. Furthermore, the ADH measurement was carried out on running engine under the full load operation. Through these results, the highly noise radiating areas on the engine surface were detected and reduced with noise shielding material. The overall engine noise level was reduced by 1.5dBA as the first stage in this noise control work.

Dynamics of a Vibratory Feeder

The most common devices used to feed small parts in an automatic assembly framework are vibratory feeders. They are used to store, feed, orientate and isolate the parts. Due to the complex mechanics of the feeding process the design of the feeders is still depending on trial and error. This paper presents a complete dynamical model of the transportation process including unilateral constraints and multiple impacts, both with coulomb friction. Some simulation results, computed with a three dimensional model, explain the practical benefit of the proposed tool.

Periodic Optimal Control of Dampers

Optimal control of dampers has been proposed to mitigate vibration effects in mechanical systems. In many cases, systems are subject to periodic forcing and the goal is to maximize the energy dissipated by the damper. In contrast to prior work utilizing instantaneous or infinite-time-horizon optimization, this paper employs periodic optimal control to maximize the energy dissipated per cycle. For single degree of freedom systems in which the maximum allowable control effort is of the same order as the forcing magnitude, a state-dependent singular control law is shown to deliver maximum energy dissipation. Alternate control laws are proposed for situations when rattlespace requirements dictate damper displacements other than that of the singular solution.

Analysis of Acoustical Properties of a Gear Mechanism

For an analysis of the acoustical properties of a multistage gear mechanism, a technique was used that combines a dynamic calculation of the mechanism as multimass multicoupling system and the SEA method for the calculation of acoustical energy. The dynamic calculation was used to determine the energy introduced into the mechanism’s gear meshes and the energy transmitted to the housing. The SEA method was used for the calculation of propagation of acoustical energy in the structure and its radiation in the surrounding space. Such a combination permits us to utilize the advantage of dynamic calculation accurately describing the mechanism’s performance and the SEA method for describing an acoustical model having the elements of high mode density in a wide frequency range. Some useful results were obtained which permit us to reduce noise level of the mechanism.