The Use of Condition Number of a FRF Matrix in Mechanical Parameter Identification

1993 ◽  
Author(s):  
Jhy-Horng Wang ◽  
Chen-Sung Liou
Keyword(s):  
Parameter Identification ◽  
Frequency Response ◽  
Condition Number ◽  
Singular Value ◽  
Measurement Noise ◽  
Mechanical Parameter ◽  
Identification Algorithm ◽  
Response Functions ◽  
Mechanical Joints ◽  
Joint Parameters

Abstract A new identification algorithm is proposed in this work to identify the parameters of mechanical joints. The method considers the whole structure as two substructures which are connected by the joints to be identified. The frequency response functions of the whole structure and substructures are used to extract the joint parameters. In contrast to the traditional methods, only a FRF matrix is needed to inverse in the proposed method. Therefore, it is possible to calculate the condition number of the FRF matrix before the identification. The condition number is defined as the ratio of the maximum singular value divided by the minimum one of a matrix. The condition number of noise contaminated FRF matrix can be used to indicate the sensitivity of the FRF matrix to measurement noise. Therefore, the condition number can be used to avoid the ill-conditioned problem by eliminating the ill-conditioned FRF in some frequency ranges before identification. The simulated results show that the proposed method can significantly improve the accuracy of identification.

Experimental Identification of Mechanical Joint Parameters

1991 ◽  
Vol 113 (1) ◽  
pp. 28-36 ◽  
Author(s):  
J. H. Wang ◽  
C. M. Liou
Keyword(s):  
Frequency Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Theoretical Simulation ◽  
Mechanical Joints ◽  
Experimental Identification ◽  
Mechanical Joint ◽  
Joint Properties ◽  
Measured Frequency Response ◽  
Joint Parameters

The dynamic behavior of a mechanical system generally are strongly affected by the properties of mechanical joints. An identification method which directly used the measured frequency response functions (FRFs) to identify the joint properties was introduced in this work. Because the measurement noise in the frequency response functions is unavoidable in practice and may lead to very faulty results, the proposed method has been developed especially to overcome this problem. The accuracy and feasibility of the proposed method were verified and demonstrated by theoretical simulation and experiments. The results show that the joint properties can be identified accurately from the FRFs even with noise effect.

Joint Parameters Identification of a Structure With Large Number of Discrete Joints

2003 ◽  
Author(s):  
J. H. Wang ◽  
S. C. Chuang
Keyword(s):  
Frequency Response ◽  
Dynamic Behavior ◽  
Error Function ◽  
Parameters Identification ◽  
New Method ◽  
Response Functions ◽  
Traditional Methods ◽  
Measured Frequency Response ◽  
Joint Parameters ◽  
Better Than

The joint parameters of a structure with a large number of discrete joints generally are very difficult to identify accurately. The difficulty is due to the fact that the dynamic behavior of a structure becomes more complex with more number of joints. A new identification method which uses the measured frequency response functions (FRFs) to identify the joint parameters is proposed in this work to overcome this difficulty. The new method uses an error function to select different best data to identify different joints so that the accuracy of the identification can be improved. The accuracy of the new method and other two traditional methods is compared in this work. The results show that the accuracy of the proposed new method is far better than other two previous methods. The proposed new method has special advantage when (1) the number of joints is large, (2) the orders of magnitude of the joint parameters are different significantly.

A Robust RCSA-Based Method for the In Situ Measurement of Rotating Tool-Tip Frequency Response Functions

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Yulei Ji ◽  
QingZhen Bi ◽  
Long Yu ◽  
Fei Ren ◽  
Yuhan Wang
Keyword(s):  
Frequency Response ◽  
In Situ Measurement ◽  
Measurement Noise ◽  
Laser Vibrometer ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Receptance Coupling ◽  
Tool Replacement ◽  
Receptance Coupling Substructure Analysis

Abstract Measuring rotating tool-tip frequency response functions (FRFs) is difficult because of the fluted tip geometry. The methods based on receptance coupling substructure analysis (RCSA) can obtain rotating tool-tip FRFs with a few tests. Existing RCSA-based methods require at least one smooth rod for measurement and then mathematically calculate the desired rotating tool-tip FRFs. However, involving the inverse of the experimentally obtained FRFs matrix, these methods are susceptible to the measurement noise in the rotating structure. In addition, the inconsistency between the holder–tool and holder–rod connections is another uncertainty which impacts accuracy. This paper presents a robust RCSA-based method to obtain rotating tool-tip FRFs. It is found that tool-tip FRFs can be calculated from another point FRFs on the same assembly. Then, one point on the smooth cylindrical shank of the tool is selected for measurement. The measured FRFs, along with those from the theoretical tool model, calculate the rotating tool-tip FRFs. Compared with the previous methods, the proposed one does not require inverting the measured FRFs matrix, inherently avoiding amplification of measurement noise. Since the tool replacement is no longer required, in situ measurement is achieved to ensure the same holder–tool connection throughout the procedure. The proposed method is first validated in a numerical case and then verified experimentally by a commercial hammer and laser vibrometer. Both results show that the method is insensitive to the measurement noise and can obtain rotating tool-tip FRFs with considerable accuracy.

The Prediction of Substructure and System Modes by the Extended Complex Mode Indication Function

1998 ◽  
Vol 120 (3) ◽  
pp. 671-677
Author(s):  
A. C. Y. Lin ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Dynamical Behavior ◽  
Singular Value ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Complex Mode ◽  
System Equation ◽  
Modal Force ◽  
Extended Complex ◽  
Value Decomposition

Yee and Tsuei (1989) developed the Modal Force Technique (MFT) as a tool for component synthesis. The approach utilizes the frequency response functions at connecting joints to predict the dynamical behavior of a synthesized system. The main difference between the MFT and the traditional impedance modeling approach is that no inversion of the frequency response functions is required for the MFT, which makes the Model Force Technique more efficient. The other major feature is that the Modal Force matrix of the synthesized system equation contains the information of both the substructure and the system modes. To determine the natural frequency and the damping of a complex mode based on the frequency response functions, the Extended Complex Mode Indication Function (Extended CMIF) technique was developed. It performs the singular value decomposition (SVD) of the Modal Force matrix at each spectral line. The peaks of the singular value plot indicate the location of the substructure modes, while the anti-peaks show the location of the system modes. This approach is simple, straightforward and can be efficiently implemented to identify complex modes.

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