利用建構滾珠研磨機的簡化數值模型模擬滾珠研磨動態，經由動態特性解析滾珠研磨的現象，作為新滾珠研磨機開發的輔助工具。
磁性流體滾珠研磨機的研磨軸高速轉動可與滾珠發生接觸滑動，得到高磨除率。定性上可由滾珠公轉和研磨軸轉速關係明顯變化,偵測接觸滑動之發生。研磨軸對滾珠的驅動摩擦力與接觸正向力、磨擦係數兩者成正比，理論上其值愈大，愈不利於滑動發生。黏度大，滾珠所受液阻力大，可促使接觸滑動發生。
磁條愈窄磁場分佈梯度愈大，浮盤等效剛性愈大，此時滾珠所受磁浮力亦較大，使與研磨軸接觸正向力較大，可得較大的磨除率。

This study makes a simple model of ball grinder to simulate the dynamics of grinding process. This theoretical analysis of the dynamic characteristics can be used to explain the phenomenon of the Kato’s experiment and it hopes to a useful tool for the design of the ball grinder.
The high removal rate is obtained with magnetic fluid grinding when high sliding velocity occurs between the ball and a high rotating drive shaft. When the balls circulation rate breaks away from the shaft speed can be used to predict the onset of skidding. Since the maximum driving friction force is proportional to contact normal force and frictional coefficient, the skidding occurs at the smaller normal force and frictional coefficient. The high viscosity of fluid, the larger fluid drag force is, when overcome the driving force then the skidding occurs.
The magnetic gradient is steeper when the width of magnet of the bed is thinner, the effects of supporting stiffness of the floating pad is higher. When the magnetic buoyant force of the ball is larger, the contact normal force is larger, then the removal rate is higher.

總目錄
中文摘要…………………………………………… i
英文摘要…………………………………………… i i
總目錄……………………………………………….iii
圖目錄………………………………………………… v
表目錄………………………………………………viii
符號表………………………………………………ix
第一章 緒論…………………………………………………… 1
1.1研究動機………………………………………… 1
1.2研究背景………………………………………… 1
1.3研究構想………………………………………… 4
1.4本論文架構…………………………………………4
第二章 滾珠研磨加工機之系統控制方程式…………5
2.1磁性流體滾珠研磨機之動態解析…………………5
2.1.1滾珠之運動方程式………………………………6
2.1.2浮盤之運動方程式………………………………8
2.2系統控制方程式……………………………………8
2.2.1系統暫態控制方程式……………………………8
2.2.2系統穩態控制方程式……………………………9
第三章磁性流體滾珠研磨機的穩態數值模型………16
3.1研磨機之系統穩態控制方程式………………… 16
3.2各作用力的計算…….……………………………18
3.3模型解析之結果及討論…………………………20
3.3.1滑動發生時的理論現象………………………20
3.3.2接觸正向力的影響….…………………………21
3.3.3摩擦係數的影響………………………………21
3.3.4黏度的影響………………………………… 21
3.3.5液阻力的影響…………………………………21
3.3.6修改滑動速度計算，在滑動發生時的理論現象…22
3.4數值模型和實驗結果差異原因之討論…… ..23
3.4.1陀螺效應之影響…………………….………… ..23
3.4.2磁浮力影響之理論解析…………………………23
3.4.3滾珠和磁性流體相對速度之解析………………24
第四章 建構磁性流體滾珠研磨機的數值模型………51
4.1研磨機之系統動態控制方程式……………………51
4.2各暫態作用力的計算………………………………52
4.2.1接觸正向力………………………………………52
4.2.2接觸摩擦力………………………………………55
4.2.3磁浮力……………………………………………56
4.2.4液阻力……………………………………………57
4.3模擬程式……………………………………………60
4.4模型校正……………………………………………61
第五章 結論與展望……………………………………70
5.1結論…………………………………………………70
5.2未來展望……………………………………………71
附錄A 非磁性物體磁浮力數值計算…………………73
參考文獻………………………………………………77

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