Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
2000-04-19
2004-01-27
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
Reexamination Certificate
active
06684168
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a technique for analyzing the rigid body displacement and the elastic vibration of a body on a global coordinate system. The rigid body displacement is displacement of the body as a rigid body, and the elastic vibration is vibration of the body as an elastic body.
2. Description of the Related Art
An important object in the design of machines having moving parts, such as automobile engines, is the reduction of vibration and noise. A more practical technique for analyzing vibration and noise with a higher accuracy is therefore desired. However, the currently employed technique of analyzing vibration of a single machine element based on its vibration transfer characteristics using multipurpose structure analysis software has been developed to near the practical use. In recent years attention has therefore been focused on development of techniques for more accurately analyzing vibration by taking into consideration interaction among a plurality of machine elements.
One of the important factors for analyzing the interaction among a plurality of machine elements is analysis of the coupling of the rigid body displacement and elastic vibration of a moving part as a body. One theory based on multibody dynamics has been postulated as one method for resolving this subject. This multibody dynamics theory was initially applied to a plurality of rigid bodies connected to one another at articulations and was integrated into a single expression using differential algebraic equations in which connection by articulation is given by constraint expressions. This multibody dynamics theory has been applied not only to rigid bodies, but also to elastic bodies by representing the elastic vibration of a body by the synthesis of elastic modes. In this multibody dynamics theory, the position of a body, direction, and elastic vibration are represented by Cartesian coordinates, Euler parameters, and modal coordinates respectively. Modal coordinates, which are used for modal analysis of elastic vibration, are defined by a plurality of modal vectors orthogonal to one another.
In the conventional body displacement-vibration analysis method based on this multibody dynamics theory, however, a plurality of different coordinate systems are used in equations of motion describing the rigid body displacement and elastic vibration of a body. This results in a high probability that, in the above equations of motion, the number of coupling terms will increase or each coupling term will become complicated, by the coupling of rigid body motion and elastic vibration. Use of this conventional body displacement-vibration analysis method therefore results in the equations of motion for analyzing the rigid body displacement and elastic vibration of a body being very complicated, such that many processes requiring a relatively long time to calculate are necessary.
Moreover, while this conventional body displacement-vibration analysis method is suitable for cases where lower-order effects of elastic vibration is considered in the motion of mechanism with multiple articulations, it is not suitable in many cases where the effect of rigid body displacement is considered in elastic vibration with a large degree of elastic freedom.
SUMMARY OF THE INVENTION
Under these circumstances, the present invention is made to provide a technique for analyzing the rigid body displacement and elastic vibration of a body suitable for cases where the effect of rigid body displacement is considered in elastic vibration with many degrees of elastic freedom. Aspects of the present invention are described below to facilitate understanding of the technical features of the present invention and provide example combinations. It should be understood that the technical features in the present specification and their combinations are not limited to these examples.
In a method according to one aspect of the present invention, a moving local observer frame located at least near a body is used as a coordinate system for observing the body independently of a global coordinate system. The local observer frame differs from the conventional body-fixed coordinate system which is fixed to a body and which must continually move along with the rigid body displacement of the body. The local observer frame must only be located relatively near the body which it observes locally.
With this method, the condition upon which modal analysis of rigid body displacement of a body is based, that the rigid body displacement is infinitesimal, will be readily met.
With this method, vibration analysis can be easily performed not only when rigid body displacement is small, but also when displacement is large.
For example, in order to analyze vibration noise of an automobile engine, it is important to consider that during engine rotation the rigid body displacement of a crank shaft relative to its cylinder blocks occurs, that an oil film is formed between bearings of these cylinder blocks and a pin on the crank shaft, that this oil film functions as a non-linear spring, and so on. In this example, the rigid body displacement of the crank shaft to the cylinder blocks is significantly large in comparison to the elastic vibration of the crank shaft. This method can be applied to vibration analysis in this example.
When analysis of displacement-vibration is performed in this way, the results obtained are usually fed back to the design of an engine to improve the structure of the crank shaft and bearings. In addition, the data will be used in the design of a suitable structure for fitting the engine onto a body and so on.
Moreover, this method can be applied to vibration analysis of a single body, such as that of a gyroscope described below, and to vibration analysis of a plurality of bodies having interaction, such as that of an engine in the above example, where the displacement of cylinder blocks to a body occurs and the displacement of a crank shaft to the cylinder blocks occurs.
That the local observer frame be located at least near a body is a requirement according to modal analysis of the rigid body displacement of a body in order to fulfill the condition that rigid body displacement be infinitesimal. For example, it can be defined as the requirement that the relative displacement of a body to a local observer frame (individual displacement vector u described below, for example) be within a infinitesimal range, or as the requirement that a body and a local observer frame substantially match.
In this method, the rigid body displacement of a body may or may not be influenced by the elastic vibration of the body. If the influence exists, rigid body displacement must be decided with analyses of the elastic vibration taken into consideration; if the influence does not exist, it is possible to decide rigid body displacement independently of analyses of the elastic vibration. Therefore, if the rigid body displacement of a body is influenced by the elastic vibration of the body, the motion of a local observer frame must be defined with the elastic vibration of the body taken into consideration, but if the rigid body displacement of a body is not influenced by the elastic vibration of the body, the motion of a local observer frame can be defined independently of the elastic vibration of the body.
Furthermore, it may be preferable that a local observer frame moves substantially along with the rigid body displacement of a body at the beginning of each observation period (start time) and moves in accordance with a function of time, independently of the rigid body displacement of the body, during each observation period except the start time. Because the local observer frame moves substantially the same as a body at the beginning of each observation period, it can be located near the body to observe the body locally during each observation period.
With this method, therefore, the modal analysis condition that rigid body displacement is infinitesimal will be readily met.
With this method, vibration analysis can be p
Aoyama Takayuki
Inagaki Mizuho
Kawamoto Atsushi
Mori Nobuyuki
Yasuda Kimihiko
Barlow John
Kabushiki Kaisha Toyota Chuo Kenkyusho
Lau Tung S
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