Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
2001-08-29
2003-06-03
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
Reexamination Certificate
active
06574570
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an approximate mode analysis method (method of approximate modal analysis) to analyze nonlinear restoring force characteristic with force-displacement hysteresis of a machine structure system. More particularly, the invention relates to the method of analysis for improving the vibration characteristic of the machine structure system by reconstructing a hysteretic characteristic using the data of a discrete load strain characteristic obtained experimentally by a vibration test or the like, alternatively, simulatively by a finite element method (FEM) analysis or the like, and by supplying an output according to the obtained data with respect to an arbitrary input.
2. Description of the Related Art
The mode analysis method has been established for its technology as a method for analyzing the vibration of the machine structure system, and has also been made commercially available as software, and frequently used. However, while the mode analysis method itself is based on a theory assuming a linear system, an actual machine structure system normally includes a plurality of nonlinear characteristics, in a bolt joined part, a sliding surface part of a baring or the like, a rotational part, a rubber pad of an engine mount as shown in
FIG. 19
, a joint of a robot, and so on.
With regard to a case including a nonlinear characteristic having no hysteretic characteristic, presented is a method for approximately achieving mode analysis by representing the nonlinear characteristic by an equivalent linearization method. This method has contributed to the rigidity designing and the working accuracy improvement of a machine tool, the support characteristic evaluation of a piping system and reflection in an aseismic designing method, optimal designing in support at the engine mount, and so on.
However, a restoring force characteristic typically represented by the rubber pad exhibits hysteretic nonlinearity. Conventionally, it was difficult to reduce an error when the estimated value obtained by estimating the frequency response characteristic of the machine structure system including such a nonlinear characteristic in a designing stage was compared with the frequency response characteristic obtained by an experiment.
When a vibration characteristic is requested by considering a structure of element, a characteristic for connecting elements together, and so on, in the designing stage, generally, analysis is carried out by using the finite element method. However, for a vibration characteristic, analysis is carried out mainly based on time history, and to obtain a frequency response characteristic, time history response must be repeated for each frequency step. Thus, a great deal of computing time is required even for obtaining the response of the linear system In addition, it is also possible to obtain a frequency response characteristic from the equation of motion. Regarding the case including the nonlinear characteristic, however, no general and simple methods have been presented to obtain the vibration characteristic of the entire machine structure system by presenting the nonlinear characteristic.
By carrying out the vibration experiment of the machine structure system, a frequency response characteristic including the above characteristic is obtained. In the mode analysis method, this is called an experimental mode analysis. According to this method, a frequency response characteristic is obtained by an experiment, and the system characteristic is improved by estimating an intrinsic frequency, a damping constant, a mass, spring, damping coefficients, and so on.
However, if the nonlinear characteristic is included, a frequency response characteristic is obtained in a biased manner from a linear characteristic. Consequently, because of a biased frequency, distortion of a characteristic in the vicinity of the intrinsic frequency, and so on, it is difficult to estimate an intrinsic frequency, and generally, a damping constant is excessively evaluated. As a result, wrong treatment has been taken for an improvement of the characteristic, or no proper treatment has been taken therefor.
With regard to nonlinear restoring force characteristic without hysteresis, a plural nonlinear simultaneous equation can be constructed by applying the equivalent linearization method to a multi-degree-of-freedom system equation of motion. It has been considered possible to find a solution of the equation, i.e., the frequency response characteristic of the multi-degree-of-freedom system including a plurality of nonlinear characteristics. In addition, by using a building block method (BB method) connected with the finite element method to connect the vibration characteristic of the device structure by the nonlinear restoring force characteristic, it has been considered possible to approximately carry out the mode analysis of the multi-degree-of-freedom nonlinear vibration system on the extension of the conventional mode analysis method.
However, the foregoing method was unable to deal with the system including the nonlinear restoring force characteristic with hysteresis, as typically seen in the rubber pad used when an automotive engine was mounted on a car body. In addition, the nonlinear characteristic of a bearing and the like was often represented by hysteretic nonlinear characteristic, and it was impossible to deal with this characteristic.
In the vibration characteristic analysis of the mechanical system, for the method of representing a hysteretic characteristic in a rigid part, a model for representing the hysteretic characteristic by a combination of divisional straight lines, such as bilinear model, a trilinear model or the like, a hysteretic characteristic model for representing it by a numerical expression, such as Ramberg-Osgood type, and so on, have been used. However, considering the simulation of the nonlinear characteristic of an actual machine based on the characteristics of such models, problems described below inevitably occur.
Each of the bilinear and trilinear models is a method for representing a hysteretic characteristic by the combination of straight lines. In these methods, the hysteretic characteristics to be represented are considered to be two and three inclined straight lines in sections respectively in the bilinear and trilinear models, and the shapes of the hysteretic characteristics are simulated by joining the straight lines over sections. A problem inherent in each of these methods is that since the hysteretic characteristic to be presented takes a complex shape, it cannot be sufficiently represented by the sectional combination of two to three straight lines.
In addition, since the hysteretic characteristic to be represented is considered to be two to three inclined straight lines, the inclination is changed piecewise. Consequently, even when the hysteretic characteristic to be represented takes a smooth shape, the sectional change of the inclination causes an output from the model to become unsmooth with respect to an arbitrary input.
There is also a problem inherent in the case of representing the hysteretic characteristic by the bilinear model. That is, when sectional straight line regression is made with respect to the hysteretic characteristic to be represented, depending on the position of inclination changing to be set, an obtained result varies even if a similar hysteretic characteristic is represented.
On the other hand, the hysteretic characteristic model represented by the Ramberg-Osgood type is a method for representing a hysteretic characteristic by a polynomial. This method is designed to simulate the shape of the hysteretic characteristic by deciding maximum and minimum coordinates based on a skeleton curve, and by connecting upward and downward curves from the coordinates. To represent the hysteretic characteristic by this method, it is necessary to match the hysteretic characteristic to be represented with the hysteretic characteristic model by using a least square method or-the like.
Irino Naruhiro
Osumi Hisashi
Sato Hisayoshi
Barlow John
Chuo University
Dougherty Anthony T.
Oliff & Berridg,e PLC
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