本研究探討深溝滾珠軸承中比較具缺陷及健康的軸承，通過模擬軸承轉動產生的振動信號。目前國內利用有限元素分析滾動軸承在有缺陷時的時域及頻域相對較少，大部分以實體軸承實驗較多，所以本文利用有限元素法商用軟體ABAQUS進行軸承滾動模擬。
為研究有故障的滾動軸承及其振動特點，分析存在缺陷的滾動軸承的頻率特徵，本次實驗針對內環的缺陷進行分析。利用前述的分析方法，本研究(一)設計以型號6205及6204之深溝滾珠軸承，利用電腦輔助設計軟體PRO-E繪製幾何外型，在所建立的內環模型上製作缺陷；(二)在ABAQUS上進行模擬分析，並同時建立時間-振幅的時域圖，並利用數據採集及信號處理，經由快速傅立葉分析提取軸承損壞元件的特徵頻率，以達到預測軸承故障進行的目的。
在變化軸心轉速、摩擦係數等相關參數來檢測參數對於模擬結果的差異性，根據對比本研究團隊過去的實驗結果，顯示有限元素模擬得到的資料分析結果與實體軸承訊號得出的量測結果相近，先得知採用摩擦係數0.08的結果最為準確。再利用此條件進行模擬分析，軸承無缺陷與分別具有內環及外環缺陷時的加速度與應力週期變化，可明顯辨識軸承的健康程度，故本研究提供一可信的軸承缺陷分析方法。

This study discusses the relatively defective and healthy bearings in deep groove ball bearings. At present, most domestic research of the rotor bearing fault focus on the experimental study, and only a few of them apply the finite element method to analyze the rotor bearing faults with respect to the time and frequency domain. Therefore, this paper uses the finite element method commercial software ABAQUS to simulate the motion of rotor bearing.
In order to study the faulty rolling bearing and its vibration characteristics, this experiment analyzes the defects of the inner ring and discusses the frequency characteristics of the defective rolling bearing. Using the aforementioned analysis methods, this study (1) uses the computer-aided design software PRO-E to draw the geometric appearance, and creates defects on the established inner ring model of 6204 and 6205; and (2) performs simulation analysis on ABAQUS and establishes a time-amplitude time domain diagram. In addition, data acquisition and signal processing techniques such as fast Fourier transform are used to extract the characteristic frequencies of bearing damage components in order to predict bearing failure.
The simulation results are compared by changing the relevant parameters such as the shaft speed and friction coefficient. According to the literature of Case Western Reserve University and the previous experimental results of this research team, it is shown that the simulation results by using finite element method are similar to those obtained from the experiment, and it is known that the most accurate result is when applying the friction coefficient of 0.08 to conduct the simulation. Using this condition for simulation analysis, the conditions of healthy bearing, inner ring defect, and outer ring defects can be clearly identified by observing the cyclic changes of acceleration and stress. Therefore, this study provides a credible bearing defect analysis method.

[1]D.SCOTT，“ Bearing Failures Diagnosis and Investigation”， National Engineering Labortory，page 199-213，1973。
[2]D.BRIE，“ Modelling Of The Spalled Rolling Element Bearing Vibration Signal : An Overview And Some New Results ”，Centre de Recherche en Automatique de Nancy,CNRS ESA 7039 Universite Henri Poincare，page 353-369，1999。
[3]趙祥，“機械原理及機械零件”，第14章-軸承，中國鐵道出版社，1998。
[4]D.HO and R.B.Randall，” Optimisation of Beearing Diagnostic Techniques Using Simulated and Actual Bearing Fault Signals “，page 763-788，2000。
[5]Z.Kiral and H.Karagülle，” Simulation and analysis of vibration signals generated by rolling element bearing with defects “，Tribology International，page 667-678，2003。
[6]朱效賢、李怡蒼、潘敏俊，”包絡譜分析於高速主軸軸承故障診斷之應用 ”，中國機械工程學會第二十二屆全國學術研討會論文集，2005。
[7]M.S.Patil,J.Mathew,P.K.Rajengrakumar,Sandeep,Desia，” A Theoretical Model to Predict the Effect of Localized Defect on Vibrations Associated With Ball Bearing ”，page 1193-1201，2010。
[8]V.N.Patel, N.Tandon, R.K.Pandey，” Vibration Studies of Dynamically Loaded Deep Groove Ball Bearings in Presence of Local Defects on Races，“International Conference on DESIGN AND MANUFACTURING, IConDM ，Volume 64, Pages 1582-1591, ISSN: 1877-7058，2013。
[9]E.Claesson，” Modelling of Roller Bearings in ABAQUS ”， Department of Applied Mechanics ,Division of Material and Computational Mechanics，2014。
[10]S.Tyagi,S.K.Panigrahi，” Transient Analysis of Ball Bearing Fault Simulation using Finite Element Method “，page 309-318，2014
[11]W.A.Smith, R.B.Randall，” Rolling Element Diagnostics Using the Case Western Reserve University Data : A Benchmark Study “，page 100-131，2015
[12]Ninkai Niu, Hongrui Cao，” A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearing with localized surface defects “，page 207-232，2015
[13]汪久根、王慶九、章維明，“ 表面粗糙度對軸承振動的影響“，
軸承2007年01期，ISSN: 1000-3762，2007。
[14]陳志忠、劉孟昆，”感應交流馬達旋轉設備振動特徵分析”，2015。
[15]A.Srivani, T.Arunkumar，”Fourier Harmonic Regression Method for Bearing Condition Monitoring using Vibration Measurements “，page 12151-12160，2017
[16]E.Kreyszig，”Advanced Engineering Mathematics”，2010。
[17]Y.Yang, W.Yang，”Simulation and Experimental analysis of Rolling Element Bearing Fault in Rotor-Bearing-Casing System“，page 205-221，2018
[18]A.Nabhan, M.Nouby，”Vibration Analysis of deep groove ball bearing with Outer Race Defect using ABAQUS “，page 312-325，2016
[19]S.Singh, G.kKopke,C.Q.Howard，”Analyses of Contact Forces and Vibration Response for a Defective Rolling Element Bearing using an Explicit Dynamics Finite Element Model “，page 5356-5377，2014
[20]湯榮濱，”振動基本原理及頻譜介紹-東培工業股份有限公司”，2006
[21]R.B.Randall, J.Antoni，”Rolling Element Bearing Dianostics-A Tutorail “，page 485-520，2011
[22]S.Singh, C.Q.Howard,C.C.Hansen，”An Extensive Review of Vibration Modelling of Rolling Element Bearing with Localized and Extended Defects “，page 300-330，2015
[23]D.Petersen, C.Howard,Z.Prime，” Varying Stiffness and Load Distributions in Defective Ball Bearings: Analytical Formulation and Application to Defect Size Estimation “，page 284-300，2015
[24]D.Zhao,T.Wang,R.X.Gao, F.Chu，” V Signal Optimization Based Generalized Demodulation Transform for Rolling Bearing Nonstationary Fault Characteristic Extraction “，2019
[25]M.Y.Toumi, S.Murer, F.Bogarg，” Numerical Simulation and Experimental Comparison of Flaw Evolution on a Bearing Raceway : Case of Trust Ball Bearing“，page 427-434，2018