Glen Prater

Eigenproblem formulation, solution and interpretation for non-proportionally damped continuous beams

Abstract A rationalized approach is described for formulating the eigenproblems associated with continuous beams where damping non-proportionalities are introduced through the use lumped dampers, partial damping layers or arbitrary complex impedances. An efficient algorithm is then presented for determining an exact solution to the resulting complex eigenvalue equations, and for computing the coefficients associated with the complex eigenfunctions. A normalization procedure is developed which embodies all pertinent modal information, yet presents the complex modes in a manner which approximates the instantaneous displacement patterns associated with the natural frequencies. This scheme also allows an analyst to assess qualitatively and quantitatively the extent of non-proportionality in the damping distribution and determine which parts of the system it most affects. The formulation and normalization techniques are illustrated with two example cases.

Finite Element Concept Models for Vehicle Architecture Assessment and Optimization

There are two distinct classes of finite element models that can be used to support vehicle body design and development. The most familiar of these is the detailed body model, which achieves computational accuracy by precisely simulating component geometries and assembly interfaces. This model type is quite useful for conducting trade-off studies after detail drawings become available. The second class is an architecture concept model that simulates the basic layout and general structural behavior of major load-carrying members (e.g., pillars, rails, rockers, etc.) and joints in the body. Such modes are valuable for design direction studies in the earliest phases of the vehicle development process. This paper presents a generic process for building architecture concept models that include a mathematical representation of the major body joints derived from existing CAE models. The difficulties involved with such joint representation are discussed, and the concept model NVH results are compared with those from a detailed body model. Although the discussion is based on a specific joint representation model, the conclusions are generic and applicable to other joint representations of the same nature.

Optical measurement of discharge valve modal parameters for a rolling piston refrigeration compressor

In this paper we describe the methodology and results of an experiment to measure the fundamental undamped natural frequency and damping ratio for the discharge reed valve in a rolling piston rotary compressor. The small size and extreme flexibility of the valve assembly required the use of a non-contacting measurement technique; thus, an optical displacement follower was chosen as the primary transducer. The measurement system also incorporated a strain gage load cell and PC-based signal processing software. The sensitivity of the system modal parameters to design variables such as valve preload geometry, lubricant viscosity, and retaining screw torque was investigated. Eventually, the measured stiffness, fundamental natural frequency and equivalent viscous damping ratio were incorporated as valve model parameters in a comprehensive computer simulation program for the compressor. Results show that this reed valve design is lightly damped, and that the fundamental natural frequency is a strong function of preload geometry. Lubricant viscosity and retaining screw torque had little effect on the modal parameters.

Development of instructional software for the calculation of form stress concentration factors

Mechanical engineering curricula include a number of required courses in solid mechanics and machine design that involve the determination of stresses in components with geometric irregularities. This article documents the development of a Windows‐based computer program, ME‐StressCon, that allows rapid calculation of form stress concentration factors and nominal stresses for a wide variety of geometry and load cases.

Gauge sensitivity indices and application for assessing vehicle body structural stiffness

Gauge sensitivity indices assess the structural performance of vehicle body architectures when subjected to changes in material thickness as a result of either same material re-gauging or material substitutions. This paper summarises the theory of gauge sensitivity indices and demonstrates the index results through a series of example cases with complex sections and different loading conditions. The results are consistent in showing that gauge sensitivity values are always greater than or equal to unity. It denotes that while low gauge sensitivity values imply a perfect structure with near-uniform internal load distribution, large values correspond to the progressive development of an internal load distribution that becomes increasingly non-uniform. The work concludes with validation case studies illustrating application of gauge sensitivity indices for assessing structural stiffness of a light-duty truck cab.

Major compliance joint modelling survey for automotive body structures

There are two distinct classes of vehicle body CAE abstractions that can be used to support vehicle body design and development, detailed models and concept models. A detailed finite element model achieves computational accuracy by precisely simulating component geometries and assembly interfaces. On the other hand, a concept model simulates stiffness behaviour of joints and major load-carrying members (e.g. pillars, rails, rockers, etc.) in a body structure. The main difference between various kinds of concept models is the representation of body joints. Joints are important components of the auto body because they affect significantly, and in some cases, they even dominate, the static and dynamic behaviour of a model. This paper reviews generic characteristics of two typical joint representation methods: a superelement elastic representation and tri-spring representation. The benefits of using a tri-spring representation over a superelement elastic representation are discussed.

Beam-Like Major Compliant Joint Methodology for Automotive Body Structures

One of major difficulties in developing and employing a concept model of a vehicle is to develop a simple and accurate model of joints. A vehicle joint is a subassembly formed by several members that intersect together. It is a thin-walled structure formed by overlapping metal sheets fastened by spot welds. The study of the joints has been important, because they can deform locally. This flexibility can affect noise, vibration and harshness (NVH) characteristics of a vehicle plus other structural performance characteristics under different loading conditions. The main difference between various kinds of concept models is the representation of body joints. Joints are important components of the auto body because they affect significantly, and in some cases, they even dominate, the static and dynamic behavior of a model. This paper introduces a new beam-like major compliant joint methodology. Joints are simulated with different parametric representations that present the major differences among various concept models. The development procedure of the beam-like major compliant joint is explained and the benefits of using this representation are discussed.Copyright

Derivation of Rigid Body Analysis Models From Vehicle Architecture Abstractions

Vehicle analysis models of every type have their basis in some type of physical representation of the design domain. Rather than describing three-dimensional continua of a collection of components as is done in detail-level CAD models, an architecture-level abstraction describes fundamental function and arrangement, while capturing just enough physical detail to be used as the basis for a meaningful representation of the design, and eventually, analyses that permit architecture assessment. The design information captured by the abstractions is available at the very earliest stages of the vehicle developing process, so the model itself can function as a “design space for ideas”. In this paper we describe a generalized process for analysis model extraction from vehicle architecture abstractions, and then apply that process to the specific case of rigid body response models. We also discuss implementation of a rigid body analysis engine that forms part of the analysis suite of a software package supporting all aspects of vehicle architecture design.Copyright

Vehicle Concept Model Abstractions For Integrated Geometric, Inertial ,Rigid Body, Powertrain and FE Analysis

Vehicle analysis models of any kind have their basis in some type of physical representation of the design domain. Rather than describing three-dimensional continua of a collection of components as is done in detail-level CAD models, an architecture-level abstraction describes fundamental function and arrangement, while capturing just enough physical detail to be used as the basis for a meaningful design space representation and eventually, analyses that permit architecture assessment. The design information captured by the abstractions is available at the very earliest stages of the vehicle development process, so the model itself can function as a “design space for ideas”. In this paper we describe vehicle architecture abstractions appropriate for integrated model extractions suitable for geometric, inertial, rigid body, acceleration, braking, fuel efficiency, structural, and NVH assessments. Additionally, we discuss the requisite level of information required for each analysis type.Copyright

An Interactive Design Space Supporting Development of Vehicle Architecture Concept Models

Due to a lack of suitable analysis tools, automotive engineers are often forced to forego quantitative optimization early in the development process, when fundamental decisions establishing vehicle architecture are made. This lack of tools arises because traditional analysis models require detailed geometric descriptions of components and assembly joints in order to yield accurate results, but this information is simply not available early in the development cycle. Optimization taking place later in the cycle usually occurs at the detail design level, and tends to result in expedient solutions to performance problems that might have been more effectively addressed at the architecture level. Alternatively, late-cycle architecture changes may be imposed, but such modifications are equivalent to a huge optimization cycle covering almost the entire design process, and require discarding the detail design work used originally as the basis of the NVH model. Optimizing at the architecture level can both shorten and improve the results of a vehicle development process. In this paper we describe the requirements and implementation of a user interface for a software package supporting vehicle architecture conceptual design and analysis.Copyright