Gearbox fault diagnosis based on bearing dynamic force identification

In this study a procedure of dynamic force identification for beamlike structures is developed based on an improved dynamic stiffness method. In this procedure, the entire structure is first divided into substructures according to the excitation locations and the measured response sites. Each substructure is then represented by an equivalent element. The resulting model only retains the degree of freedom (DOF) associated with the excitations and the measured responses and the DOF corresponding to the boundaries of the structures. Because the technique partly bypasses the processes of modal parameter extraction, global matrix inversion, and model reduction, it can eliminate many of the approximations and errors that may be introduced during these processes. The principle of the method is described in detail and its efficiency is demonstrated via numerical simulations of three different structures. The sensitivity of the estimated force to random noise is discussed and the limitation of the technique is pointed out.

Download Full-text

Dynamic Force Identification in Peripheral Milling Based on CGLS Using Filtered Acceleration Signals and Averaged Transfer Functions

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4043362 ◽

2019 ◽

Vol 141 (6) ◽

Cited By ~ 1

Author(s):

Chenxi Wang ◽

Xingwu Zhang ◽

Baijie Qiao ◽

Hongrui Cao ◽

Xuefeng Chen

Keyword(s):

Time Domain ◽

Transfer Functions ◽

Milling Process ◽

Dynamic Force ◽

Band Pass Filter ◽

Peripheral Milling ◽

Milling Force ◽

Force Identification ◽

Milling Forces ◽

Acceleration Signals

Dynamic milling forces have been widely used to monitor the condition of the milling process. However, it is very difficult to measure milling forces directly in operation, particularly in the industrial scene. In this paper, a dynamic force identification method in time domain, conjugate gradient least square (CGLS), is employed for reconstructing the time history of milling forces using acceleration signals in the peripheral milling process. CGLS is adopted for force identification because of its high accuracy and efficiency, which handles the ill-conditioned matrix well. In the milling process, the tool with high-speed rotation has different transfer functions between tool nose and accelerometers at different angular positions. Based on this fact, the averaged transfer functions are employed to reduce the error amplification of regularization processing for milling force identification. Moreover, in order to eliminate the effect of idling and high-frequency components on identification accuracy, the Butterworth band-pass filter is adopted for acceleration signals preprocessing. Finally, the proposed method is validated by milling tests under different cutting parameters. Experimental results demonstrate that the identified and measured milling forces are in good agreement on the whole time domain, which verifies the effectiveness and generalization of the indirect method for milling force measuring. In addition, the Tikhonov regularization method is also implemented for comparison, which shows that CGLS has higher accuracy and efficiency.

Download Full-text

Industry-Oriented Method for Dynamic Force Identification in Peripheral Milling Based on FSC-LSQR Using Acceleration Signals

10.21203/rs.3.rs-1218168/v1 ◽

2022 ◽

Author(s):

Maxiao Hou ◽

Hongrui Cao ◽

Qi Li ◽

Jianghai Shi

Keyword(s):

High Efficiency ◽

Machining Process ◽

Qr Factorization ◽

Calculation Error ◽

Dynamic Force ◽

Milling Force ◽

Force Identification ◽

Online Identification ◽

Ill Posed ◽

Acceleration Signals

Abstract Online measurement of milling force play a vital role in enabling machining process monitoring and control. In practice, the milling force is difficult to be measured directly with the dynamometer. This paper develops a novel method for milling force identification called least square QR-factorization with fast stopping criterion (FSC-LSQR) method, and the queue buffer structure (QBS) is employed for the online identification of milling force using acceleration signals. The convolution integral of milling force and acceleration signals is discretized, which turns the problem of milling force identification into a linear discrete ill-posed problem. The FSC-LSQR algorithm is adopted for milling force identification because of its high efficiency and accuracy, which handles the linear discrete ill-posed problem effectively. The online identification of milling force can be realized using the acceleration signal enqueue and the milling force dequeue operations of the QBS. Finally, the effectiveness of the method is verified by experiments. The experimental results show that the FSC-LSQR algorithm running time is within \((0.05s)\) and the calculation error is less than \((10\%)\). The proposed method can make the sampling frequency of the milling force reach 10240Hz by employing QBS, which satisfy the industry requirements of milling force measurement.

Download Full-text

A Novel Method of Dynamic Force Identification and Its Application

Mathematical Problems in Engineering ◽

10.1155/2019/1534560 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Nengjian Wang ◽

Qinhui Liu ◽

Chunping Ren ◽

Chunsheng Liu

Keyword(s):

Conjugate Gradient ◽

Optimization Problems ◽

Stability And Convergence ◽

Future Research ◽

Dynamic Force ◽

Force Identification ◽

Unconstrained Optimization Problems ◽

Practical Engineering ◽

Gradient Parameter ◽

Spectral Conjugate Gradient

In this paper, an efficient mixed spectral conjugate gradient (EMSCG, for short) method is presented for solving unconstrained optimization problems. In this work, we construct a novel formula performed by using a conjugate gradient parameter which takes into account the advantages of Fletcher–Reeves (FR), Polak–Ribiere–Polyak (PRP), and a variant Polak-Ribiere-Polyak (VPRP), prove its stability and convergence, and apply it to the dynamic force identification of practical engineering structure. The analysis results show that the present method has higher efficiency, stronger robust convergence quality, and fewer iterations. In addition, the proposed method can provide more efficient and numerically stable approximation of the actual force, compared with the FR method, PRP method, and VPRP method. Therefore, we can make a clear conclusion that the proposed method in this paper can provide an effective optimization solution. Meanwhile, there is reason to believe that the proposed method can offer a reference for future research.

Download Full-text

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Mathematical Problems in Engineering ◽

10.1155/2019/6095184 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Chunping Ren ◽

Nengjian Wang ◽

Qinhui Liu ◽

Chunsheng Liu

Keyword(s):

Kernel Function ◽

Tikhonov Regularization ◽

Regularization Method ◽

Integral Form ◽

Identification Problem ◽

Tikhonov Regularization Method ◽

Dynamic Force ◽

Conical Pick ◽

Force Identification ◽

Green Kernel

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal-seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill-conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill-posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

Download Full-text

Importance of Selecting a Suitable Analysis Frequency Range in Impact Force Identification for Automobile Test Rig

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.663.88 ◽

2014 ◽

Vol 663 ◽

pp. 88-92

Author(s):

Khoo Shin Yee ◽

Ong Zhi Chao ◽

Kong Keen Kuan ◽

Zubaidah Ismail ◽

Chong Wen Tong ◽

...

Keyword(s):

Impact Force ◽

Excitation Frequency ◽

Time History ◽

Transformation Method ◽

Dynamic Force ◽

Frequency Range ◽

Test Rig ◽

Force Identification ◽

History Of ◽

The Impact

In this study, the effectiveness of selecting a suitable analysis frequency range in impact force identification is highlighted. A methodology that utilizesOperating Deflection Shape (ODS) analysis, Modal Analysis (MA) and Modal Transformation Method (MTM) to evaluate the dynamic force in three cases of analysis frequency ranges was presented. These three cases are the over-estimated, even-estimated, and under-estimated cases, which consist of higher, similar andlower analysis frequency range respectively, compared to the actual excitation frequency range. The performance of this approach was demonstrated via experiment. A Perspex plate with four ground supports was used as the automobile test rig. By measuring the acceleration response and Frequency Response Function (FRF) of the test rig, the time history of unknown force was recovered by the proposed method where the impact location was known in advance. It showed that the force identification result for even-estimated case falls within acceptable range while the force identification result for over-estimated and under-estimated cases isnot acceptable

Download Full-text

Identification of Random Dynamic Force Using an Improved Maximum Entropy Regularization Combined with a Novel Conjugate Gradient

Mathematical Problems in Engineering ◽

10.1155/2017/9125734 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 5

Author(s):

ChunPing Ren ◽

NengJian Wang ◽

ChunSheng Liu

Keyword(s):

Maximum Entropy ◽

Conjugate Gradient ◽

Regularization Parameter ◽

Engineering Application ◽

Optimal Solution ◽

Identification Problem ◽

Dynamic Force ◽

Force Identification ◽

Mathematical Algorithm ◽

Practical Engineering

We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME) regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG) method was applied to solve the objective function, which was abbreviated as IME-NCG algorithm. The result of IME-NCG algorithm is compared with that of ME, ME-CG, ME-NCG, and IME-CG algorithm; it is found that IME-NCG algorithm is available for identifying the random dynamic force due to smaller root mean-square-error (RMSE), lower restoration time, and fewer iterative steps. Example of engineering application shows that L-curve method is introduced which is better than Generalized Cross Validation (GCV) method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill-conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.

Download Full-text

A novel strategy for force identification of nonlinear structures

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/14613484211033433 ◽

2021 ◽

pp. 146134842110334

Author(s):

Jie Liu ◽

Tianqi Ding ◽

Shanhui Liu ◽

Bingbing Hu

Keyword(s):

State Space ◽

State Space Model ◽

Dynamic Force ◽

Nonlinear Structures ◽

Nonlinear Structure ◽

Force Identification ◽

Space Model ◽

Excitation Force ◽

Nonlinear State ◽

Identification Strategy

Dynamic force is the key indicator for monitoring the condition of a mechanical product. These mechanical structures always encompass some nonlinear factors. Most previous studies focused on obtaining the dynamic force of linear structures. Consequently, this study focuses on the nonlinear mechanical structure, and a novel identification strategy is proposed to indirectly identify the excitation force. For the identification strategy, based on a nonlinear state-space model, a force identification equation for the nonlinear structure is built, wherein the transfer matrix consists of coefficient matrices of the nonlinear state-space model, and these coefficient matrices are calculated by a nonlinear subspace identification algorithm. Then, under the generalized cross-validation criterion, the truncated total least squares method is introduced to solve the ill-posed equation to eventually obtain the excitation force of the nonlinear structure. The identification results from two numerical simulation cases and one experimental case illustrate that the proposed identification strategy can stably and accurately identify the excitation force of nonlinear structures.

Download Full-text

Force identification based on the reconstruction of distributed response with an optimized sensor placement

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406218756445 ◽

2018 ◽

Vol 233 (1) ◽

pp. 108-119

Author(s):

Hao Jiang ◽

Haijun Wu ◽

Liang Yu ◽

Weikang Jiang

Keyword(s):

Sensor Placement ◽

Gaussian Quadrature ◽

Dynamic Force ◽

Response Distribution ◽

Identification Procedure ◽

Structural Dynamic ◽

Force Identification ◽

New Perspective ◽

Spatial Locations ◽

Influence Of Noise

The errors of the force identification vary with different spatial locations of the response measurements on machinery. This investigation proposes a method to identify the structural dynamic force with the use of the distributed response. An optimized sensor placement is obtained by using a set of local orthogonal polynomials to approximate the response distribution of the chosen region and choosing the Gaussian quadrature points as the sensor locations. Then the forward model based on the reconstruction of distributed response is established and the dynamic force can be obtained by an appropriate regularization method. Numerical simulations of models with planar and curved surfaces are presented to validate the method. It is found that the proposed method can effectively reduce the influence of noise and improve the precision of the force identification. The method is also validated by an experiment and an accurate recognition of the forces is observed. This paper provides a new perspective on the force identification procedure based on the distributed response.

Download Full-text